I am currently working with David Aristoff and Olivier Pinaud. We study convergence rates and spectral properties of Bayesian sampling algorithms and Markov processes.
My recent publication with David Herzog, Gabriel Stoltz, and Maria Gordina establishes explicit rates of convergence for Langevin dynamics subject to singular potentials in a weighted norm.
More recently, with David Herzog, we have proven on the asymptotic behavior of degenerately stochastically forced Lorenz 96 systems.
My mathematical research and interests lie in:
Chaos Theory and Nonlinear Dynamics
Partial Differential Equations
A recent presentation of our Langevin dynamics results.
Research with Undergraduates
I was privileged enough to participate in mathematics research as an undergraduate at Concordia College, as well as through an NSF-funded research program at New York University. These experiences were invaluable to my future career as a mathematician, and I try to participate in leading undergraduate research whenever possible. The list of program topics I have led with undergraduates includes:
Fractals and iterated function systems
Sampling and interpolation theory
Markov chains and mixing times
Models for turbulent flow
Fractional operator theory